SUMMARYA new finite element method is devised for the numerical solution of elliptic boundary value problems with geometrical singularities. In it, the singularity is eliminated from the computational domain in a n exact fashion. This is in contrast to other common methods, such as those which use a refined mesh in the singularity region, or those which use special singular finite elements. In them, the singularity is treated as a part of the numerical scheme. The new method is illustrated on an elliptic differential equation in a domain containing a re-entrant corner. Numerical experiments show that the new method yields results which are generally much more accurate than those obtained by using the standard finite element method with mesh refinement in the singularity region. Both methods require about the same computing time.

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An ef®cient ®nite element scheme is devised for problems in linear viscoelasticity of solids with a moving boundary. Such problems arise, for example, in the burning process of solid fuel (propellant). Since viscoelastic constitutive behavior is inherently associated with à`m emory,'' the potential need to store and operate on the entire history of the numerical solution has been a source of concern in computational viscoelasticity. A well-knowǹ`m emory trick'' overcomes this dif®culty in the ®xed-boundary case. Here the``memory trick'' is extended to problems involving moving boundaries. The computational aspects of this extended scheme are discussed, and its performance is demonstrated via a numerical example. In addition, a special numerical integration rule is proposed for the viscoelastic integral, which is more accurate than the commonly-used trapezoidal rule and does not require additional computational effort.

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